Will some players always underachieve?

We had an interesting comment from a reader this week regarding the visualization posted plotting actual points with expected points. My proposition was that the players whose xP trailed their actual points by a distance were likely undervalued by the market, and while we wouldn't suggest they will somehow "make up" those points left on the table to date, we would expect their production to take an uptick assuming they continue to get chances and playing time at a relatively consistent rate. The reader had a different view:

"When I look at this chart I don't see underperformers or overperformers all I see is players on form who are capitalising on their chances (Ramsey and Rooney) and players who are of such quality that they will always out perform the normal (Aguero and Yaya) . . . I believe that if you reconstructed this table after xmas with a start date of tomorrow then the same players would occupy the two sides."

It's a fair proposition and one I wanted to examine further. I think there's a general discomfort with the idea of regressing players' production to the mean as it seems to suggest they are all created equally. A couple of responses to that:

1. For conversion rates which appear to be repeatable year on year, such as shot on target percentage (SoT%), we regress players to their own historical rates (where available). This means that if we say Olivier Giroud has an unsustainable SoT%, we're not saying his is too high compared with Danny Graham or Frazier Campbell, we're saying it's way above his own historic rate.
2. For conversion rates where we do regress to a league average (or at least use league average in a weighted average), it's because I haven't seen any evidence that players can consistently perform above the average in that given rate. The classic example is goals per shot on target (G/SoT) which tends to regress close to a mean for most players, with only a couple exceeding the average for more than a couple of years in a row (and that would be expected even if we were talking about a totally random event). There might be some repeatability there, but it's a lot less than most would expect based on purely on notions like "form", "class" or being "clinical".

The good news is that this is fairly easy to test. Below we've plotted players' +/- score as of this week (which shows the difference between their actual and expected points with a positive score meaning their expected exceeds their actual) against the same metric from the midway point of last season. I picked that point in time based on the reader comment about Christmas but I'm fairly confident a similar conclusion could be drawn from pretty much any two comparable samples:

Learn About Tableau

The first observation is that we see very little correlation from year to year. 10 players outperformed their points total last season by at least 10 points, yet only one of these (Podolski) has managed to outperform his total to date by even 5 points. Similarly, eight players underperformed their underlying stats by 10 or more points last season, and of these two (Lambert and Cisse) have once again failed to match their live up to expectations. On the flip side we've seen players like Aguero, Rooney, Lallana, Suarez, Michu, Walters and Fellaini benefit or suffer from huge reversals in fortune over the two samples.

One of the things I love about sports writing is that it can be a gateway into so many interesting subjects, and while I'm not learned enough to talk about most of them here, I would venture that there is an element of bias regarding the way we judge the above. When a player like Ramsey explodes in a small sample, we tend to quickly absorb that information into our collective psyche and it becomes the new self evident truth that he is a great player (despite several seasons of reasonable yet unspectacular play, at least from a fantasy perspective). We then place too much weight on these recent events, much like how people stop swimming after a shark attack, despite the fact there are countless things more likely to really kill them that they ignore every day. I believe the term for this specific type of bias is referred to as the availability heuristic.

In the chart we see Aguero has the second highest +/- score for 2013 and one could rationalise that being due to his superior skill and quality teammates. Indeed, that's possibly true to a point. However, he had those very same skills and most of the teammates last year too, yet was actually one of the biggest underperformers last year, serving as a constant source of frustration for his owners. Or take van Persie. Last year he ascended to a new level and was casually thrown into conversations alongside the best in the world, and thus the fact he outperformed his xP by a full 13 points through half a year could be discounted as him simply being better than everyone else. Fast forward 10 months and we have a player who has only just caught up to his xP total for the year, having suffered through some bad luck these past couple of months.

As a final check, the colour coding relates to the players' team's league position ranging from 1st (green) to last (red). I wondered if we'd tend to see players from the better teams show an ability to repeat positive seasons as they benefit from more quality chances per game. I guess this works to a degree in that those in the bottom left quadrant generally play for better teams, yet there's not enough here to really draw any solid conclusions.

It's always good to challenge forecasts like the ones you find in these pages - especially the ones found in these pages! - but caution should also be exercised when dismissing data which contradicts our current view of the game. There are certainly aspects of a player's game which can consistently be above average (SoT% for one) but others seem far less repeatable. The current iteration of the model adjusts for these differences and thus that's why we're going to see turnover in the players who over or underachieve expectations. 

Model review: Gameweeks 8-17

As promised, it's time to take a step back from forecasting and projecting and look at how the model has performed since I rolled it out in Gameweek 8. There are three ways to look at this:

1. Look at each player's weekly forecast score versus their actual weekly score
2. Look at each player's aggregated forecast score versus their actual aggregated score
3. Look at each player's average forecast score (per 90 minutes) versus their average actual score

Each measure has it's advantages and disadvantages but I will throw the first option out as any model is simply not going to be accurate enough on a weekly basis enjoy great success. Of course, we can use its outputs to forecast the probability of different players' chance to succeed but even if it was perfect we'd still see massive fluctuations. So that leaves options two and three which each have some advantages: option two is the truest comparator of how the model performed over the period while option three does a better job at accounting for the fact that players don't play every week. As a compromise, I am comparing points on a total basis but I've thrown out all games where players played 45 minutes or less as they tend to mess up the correlation stats and aren't really representative of what the model is trying to achieve. Trying to forecast decisions by the likes of Mancini need a more powerful computer than a MacBook.

Powered by Tableau

I'm not going to run through individual players but if you would like to discuss a player in more detail, feel me to do so in the comments. A few high level points:

1. The model seems to be performing quite well, and if we limit ourselves to players who have racked up 450 or more minutes, we see a 70% correlation and 0.5 r-squared which are reasonable (though hardly indicative of a perfect model)
2. The fact that the line intersects the y-axis at ~three points suggests that the xP measure is probably underestimating scores across the board. This is reasonable for a couple of reasons. One, the model is based on average outcomes and thus will never forecast the kind of 23 point performance we saw from Cazorla this week. Second, I currently crudely account for bonus points by simply awarding 1.5 points per goal (the average points earned for a goalscorer). In reality of course, a goalscorer will often earn all three points for a scoring effort which can impact scores here, particularly at the top end of the market.

The main trend most people will observe is that the 'elite' players are above the line and thus the model is tending to undervalue them. In some ways, mainly due to the aforementioned issues in point two above, this is true and I'd be happy to concede that some more work is needed to better apportion bonus points (which will overwhelmingly flow to elite players) and perhaps reduce the regression rates if we can establish that the elite players really can exceed league average in terms of goals per shot on target with any true consistency. 

That said, we need to be careful not to get caught up in confirmation bias by anointing those players with high scores as 'elite' (are we doing so because of their talent of because of their recent points hauls?). Rooney and van Persie are obviously some of the league's best players but it's fair to say that Fellani and Michu wouldn't have been in that conversation at the start of the season, while many were getting frustrated with Cazorla until his huge haul this week. While there's no doubting there could be something here, other 'elite' players like Suarez, Ba and Hazard have essentially performed in line with the model, with Aguero significantly below, so it's overly simplistic to simply state that the model is too harsh at the top end of the market. 

In terms of using this information, this graph should not necessarily be used as a indication of future regression. For example, if a player steadily increased his shot production over this period, the model would always be behind in terms of forecasting his production and by the end of the period his points would reasonably (and sustainably) outshine his xP. It can however be used to spark those conversations though, and to help us look into players who might regress, but it's not as simple as everyone regressing towards that trend line.

Overall, I'm pleased with these results and they form a good starting point for future developments. If we look at the distribution of variances we see that they form somewhat of a familiar bell curve, without too many huge variances at either end of the spectrum. 79 of the 104 players in the sample fell within 10 points of the expected points, which isn't too bad over a 10 week period. 

The next step is look at tweaking the formulas to try and understand those variances at the top end of the chart and determine how much of the difference is attributable to their true skill exceeding the average and how much is attributable to confirmation bias and revisionism. As always, any suggestions are welcome, and I'll do another update like this in a few weeks to report back on any updates or developments.

Regression to the mean: goals per shot on target

The purpose of this post is two-fold. First, I want to illustrate a point I've made before in graphical form and highlight a couple of players coming out of that analysis. Second, I want to give a little bit of narrative around regression to the mean and issue a word of caution as to where I'm seeing it misapplied fairly regularly in these stat-friendly times.

From some quick research over the top forwards in the league, we see that, generally, they haven't really shown an ability to consistently convert shots on target (SoT) into goals above the league average rate. The league average hovers around the 33% mark for forwards and 28% mark for midfielders, with very few players able to exceed those totals each year (and even then that would be expected purely based on statistical variance). In short then, whether it seems intuitive or not, if a player's SoT are turning into goals at a very high rate, we must expect some regression in the coming weeks.

Now then, a quick side bar as to what we mean by this, as this term is often misused and the difference can appear trivial but is actually key (long term readers will know that I too made this mistake once myself so this isn't the rant of a classically trained statistician, outraged that the masses are misusing his darling tools, more a warning message for those trying to use statistical analysis a bit more in their weekly decision making).

The first point is that regression accounts for what should happen in the future and has no interest in correcting for past anomalies. Take, for example, the basketball player with a career free throw percentage of 80% who hasn't suffered any significant ageing or reasons for decline/improvement. If, after half a season he's taken 100 free throws and made 70 of them (70%) what do we expect from his second half? To get his year end average back up to his career 80% rate he'd have to go 90/100 to give him 160/200 for the year, or 80%. But, on what basis will he suddenly perform above his career rate? Averages and regression care not for your 82 game sample size (or, in our case, 38 games) and thus it's simply not true to say we expect his season rate to regress all the way back to his 80% conversion rate. Instead, we expect the rest of the season to see him convert at his true talent level of 80%.

Let's look at a football example for clarity. Through eleven gameweeks, Wayne Rooney has hit the target 12 times and scored twice (17%). To get back to that 34% mark noted above, Rooney would have to convert six of his next 12 shots to give him the eight goals needed from 24 shots (33%), but that's not what we expect. We expect him to convert at that same 33% rate so four of his next 12 shots would be goals. This may sound pedantic but just in this crude example it's the difference between Rooney scoring four and six goals over a relatively short time frame and can obviously have a large impact on our forecasts.

We can however say that if player x is getting a lot of shooting opportunities and continues to do so, he should convert at a better rate than he has to date and thus appears undervalued by the market. It's a subtle distinction but an important one that needs making every now and again.

The second, and somewhat trivial point to make is that regression goes both ways so Rooney's conversion rate can regress up to the mean, rather than always having to cite the Steve Fletchers of the world whose conversion rate looks unsustainable and thus is pegged fro downwards regression.

Okay then, onto some data.

The below chart plots players' total shots per 90 minutes on the x axis against their goals per shot on target percentage on the y axis. The lines mark the league average for both measures for all forwards this year (the G/SoT%  includes several years' data):

Powered by Tableau

If you're below the line you've converted SoT into goals at a lower than expected rate and thus have the potential to be undervalued by the market. Those in the bottom right quadrant are particularly attractive as by taking more shots per game we (a) have a larger sample size to suggest they've been - for want of a better word, "unlucky" - and (b) they should get more opportunities to enjoy more league average success in the future. Indeed, this quadrant consists of several players I've highlighted of late, led by Rooney and Aguero but also recent Moneyball candidate Cisse and a couple of players who've made appearances in a couple of fanning the flames like Giroud and Benteke.

The bottom left if harder to be excited about as while they should convert at a higher rate in the future, their overall lack of chances may ultimately mean it doesn't make too much difference and thus they're tough to own. This is particularly true of someone like P Cisse, as while he appears to have been unfortunate in converting his chances, even at a league average rate he would have scored only one more goal, clearly not enough to justify his lofty price tag.

The top left quadrant is the real concern as this group appears to have overachieved versus league average in terms of G/SoT% so unless you believe they have a genuine skill to continue to do so, we're expecting some regression in the coming weeks and months. Fletcher is the stand out man here whose 63% conversion rate is clearly unsustainable, even for a player who has shown an ability to exceed the league average over the years. This data needs to be taken in context as someone like Crouch could still offer some value if he converted at a lower rate but care should be taken before we anoint anyone from this group as great fantasy options.

The top right quadrant is a mixed bag and one you'd label with 'caution' rather than a full on 'warning'. Take Berbatov for example. With five goals from just 11 SoT, his 45% rate looks a touch high and of his next 11 SoT we'd expect only 3.6 to hit the back of the net. However, for a cheaper player who comes with job security, genuine talent and who's getting more than the average total shots per game, that rate would still potentially make him good value and forecast him for a further 14 goals if he played every game from here on (1.57 SoT/90minutes x 27 games x 33% conversion rate). The caution more comes within players like Suarez or even the great van Persie who are getting a lot of hype and, while excellent prospects, might be getting a touch overvalued based on their production to date. Again, it's all relative as using the same calculation as for Berbatov, van Persie would still be on pace for another 13 goals even at a league average rate, but that is substantially less than some are foreseeing.

One final note here. You might wonder why I'm plotting SoT% against total shots per 90 minutes rather than only shots on target. It's a valid point but I've used total shots as my concern with only using SoT is that the sample sizes are so small that extrapolating them can get messy quickly. I'm more comfortable therefore to add the required note that not every shot is created equal, rather than relying on Benteke's six SoT and drawing too many inferences (with 24 total shots and 22 SiB one can expect a better on target rate in the future too).

As with pretty much every piece of analysis I post, other than the final model forecasts, the above should not be taken as 'sell player x' or 'buy player y' but more a way of identifying players to look closer at, one way or another. It doesn't, for instance, factor in strength of schedule played or upcoming, assist potential and a myriad of other factors, so it shouldn't be taken out of context. I like it's visual simplicity though and it's nice way to identify players and think "I didn't realise player x was benefiting from high shot conversion, maybe I should look closer at his stats". 

Forecasting player performance: goals

WARNING: This post is going to skew long and won't contain any directly relevant fantasy advice to help you make your transfers this week. It might get a bit nerdy at times, though I'm far from classically trained in statistics so the concepts, if not always the terminology, should be accessible to all. I also won't reach any definitive conclusion as these models are a work in progress. Any input on anything not considered below or anywhere where you disagree with any conclusions can be posted in the comments or over at Shots on Target where you'll find a handy forum to discuss these issues. We're also only looking at forecasting goals here, assists will need a separate post.

Tracking historic success
The way I look at it, there are three distinct ways to track historic success:

• Historic classic stats (goals, assists etc)
• Historic fantasy points (similar to classic stats but accounting for all fantasy relevant events)
• Historic underlying stats (a much deeper understanding of a player's performance including his involvement in different areas of the field, his shots taken, where those shots were taken from, his passes completed etc).

If you've made it this far you're probably comfortable with the fact that the latter is the most useful but you'd be amazed with how many comments I see that player x is in 'form' or that player y is likely to score, essentially based on one or two games in recent memory of either scoring or not.

I must admit that I struggle a bit here as it seems odd to totally ignore production to date when we still aren't totally certain about the relationships we'll explore below. If you were forecasting the chance of a die landing on '4' then, of course, historic data is totally useless, the odds are still 1/6. However, if you were unsure whether or not the die was loaded you might want to adjust your 1/6 estimate at some point once the data sample became significant. We don't have 'loaded' fantasy players but we do have outliers who have consistently shown an ability to out (or under) perform their underlying stats and thus taking some account of the historic production could act as a safety net to make sure we don't judge these players incorrectly. It's not an ideal solution and I'm still not sure if it's required but I do think this data at least deserves to be addressed rather than being simply discounted as unreliable.

Projecting future success
So what do we want to know about an individual player to help us forecast his future success? A few considerations:

1. How many, and what kind of, scoring opportunities is he getting each game?
Through three games this year, Michu had registered 8 shots, 4 of which were on target and all of which hit the back of the net. We will often comment that such a conversion rate is 'unsustainable', but what exactly does this mean? Well, the fact that Michu has hit the target 50% of the time looks about right and shouldn't be of concern. Last season midfielders hit the target around 44% of the time and it's reasonable to suggest that Michu is at, or above, league average. We'll get into individual adjustments below in point 2, but for now, we can conclude that this rate is roughly acceptable. The issue however is Michu's 4 goals from just 4 shots on target. Last season, midfielders converted shots on target to goals at a rate of 25% so we would have expected Michu to have just a single goal, not the four he has registered at this point. We would therefore conclude that, if Michu continues to get chances at his current rate, he should regress to the mean in the coming weeks and won't perform at the same rate as he has to date. Note that we are not saying everything will equal out so that over the season he will necessarily have converted 25% of his shots on target into goals, only that that is the expected outcome from here on.

Now, the next issue to consider is what kind of shots a player is getting. This is intuitive as shots in the box will obviously be converted at a higher rate than those from long range, but this point really needs to be emphasised when you consider the differences. The below table shows the percentage of different shot types converted to goals last season:

	Midfielders	Forwards
Total shots - inside box	18%	20%
Total shots - outside box	5%	7%
Shots on target - inside box	35%	39%
Shots on target - outside box	14%	17%

Table 1 - Conversion rates of shot types by position. Generated with HTML Tables

We can see that the differences are dramatic and thus we need to be careful when looking at total shots for players like Cazorla, who are prone to take a pop from well outside the area. Of course, he's very capable of hitting the back of the net from 30 yards, but even the most optimistic of Cazorla fans would have to concede that Fellaini's 30 total shots are quite a lot stronger than Cazorla's, when you factor in that 25 of Fellaini's were taken inside in the area compared to just 10 for the Spaniard. Indeed, using the averages above, and ignoring shots on target for a second, Cazorla would be expected to have scored 2.75 goals (10 shots inside the box*18% + 19 shots outside the box*5%), compared to 4.75 for Fellaini (25*18% + 5*5%).

One potential solution to the above dilemma is to purely look at shots on target, which have the strongest correlation to goals over the course of a season. The correlation between different player stats and goals last season are shown below:

Player Stat	Correlation
Shots on target	91%
'Big chances' (per Opta)	90%
Shots inside the box	87%
Total shots	86%
Touches in opponents' box	78%

Table 2 - Correlation between different player stats and goals. Generated with HTML Tables

Long term I think that exclusively looking at 'shots on target' could be the right answer, but I believe a small adjustment is needed when dealing with small sample sizes. Consider, for example, Papiss Cisse through seven weeks this season. He's registered a very useful 16 shots (12th among forwards), but has managed to hit the target just 4 times (t28th), not scoring in the process. Looking purely at shots on target would suggest that he 'should' have scored somewhere between one and two goals, depending on how clinical you believe he can really be (league average is somewhere around 34% but last season Cisse scored with 57% of all shots on target). The issue is that last season he hit the target with 54% of his shots, and did so with 46% of his shots in the Bundesliga with Freiburg. Therefore, it's likely that his 25% hit-the-target-rate should also improve, perhaps to as high as 50%, which would give him a projected eight shots on target for the year and thus an expected goal haul of between two and four for the year to date. Either way the data suggests he is due for some positive regression, the way we split it just dictates how much.

I would understand if others were keen to just look at shots on target but given the above, so long as we're dealing with small sample sizes, I plan to add a thin layer to the projection model to account for total shots, taking note however to adjust at the lower of a player's hit-the-target rate and the league average (this should hopefully take care of the likes of Suarez, who's never seen a shot he wouldn't take and historically has a poor on-target rate of 36% while at Liverpool).

2. How has he converted these chances in the past?
Let's go back to Cisse for a second. He has 16 shots with 4 on target but has yet to register a goal. We've acknowledged that the outcome likely doesn't match the process if we took his data over a larger sample size, but how can we adjust it? In short we have two options:

1. adjust player data based on league average conversion rates
2. adjust player data based on their own individual historic rates

Ideally we'd use the latter for everyone as it's simply not realistic to assume all players are the same, particularly when it comes to actually hitting the target (what happens after you hit the target seems to be more reliant on luck as even the elite players tend to have peaks and troughs, but even so, skill is clearly a factor). The problem though is sample size, or more precisely, useful sample size. Going back to Cisse, how do we deal with his shot data from Freiburg (a mid table team in a good league) or Metz (at the time in the French second tier)? If we simply discount that data then we're left with 13 league games from last season, in which Cisse posted a historically good (and almost certainly unsustainable) conversion rate.

For better or worse, I think for players like Cisse we're left with no choice but to simply use a league average rate. We could consider having different rates for players with varying profiles, but then you get into a potential mess where we're applying judgements on whether Cisse (recently deployed out wide) is a wide forward of a true 'striker' and thus the whole system could get clouded.

To continue using Cisse as the subject, we'd get the below 'expected' goals:

1. League average rate (table 1): 14 shots inside the box*20% + 2 shots outside the box*7% = 2.9 goals
2. Cisse's individual on-target rate: 16 total shots*50% on target rate*39% (table 1) = 2.5 goals 

What then, for players like Fernando Torres, for who we have a reasonable amount of Premier League data? Here I believe we need to use judgement but, for starters, we can take his 28(18) appearances in a Chelsea shirt in the league and in this case add in his time at Liverpool too. If we were trying to forecast every player we'd need to set a fixed set of parameters here, but in reality we are probably comfortable using league average rates for the vast majority of players and then individually deciding historic rates for those players under captain consideration (ie the elite). To finish the example, Torres recorded above average rates while at Liverpool, hitting the target with 47% of his shots, scoring on 19% of all shots and 41% of those on target. At Chelsea - as expected- his numbers have decreased so that he hits the target on just 28% of shots, scoring 8% of all shots and 28% of shots on target. Using the sum of all these gives you rates of 43%, 17% and 39% which are at, or just above league average. This feels about right given the way Torres has displayed elite skills in the past (and he's just 28 remember) but has struggled in a Chelsea shirt for the large part. I would therefore be happy going with these individual marks to assess Torres' outlook.

The observant reader will note that, even when looking at Cisse's own individual on-target rate, I have still used the league average conversion rate to see how many goals he ultimately is forecast to score. I've settled on that approach because, in my research to date which I will repost soon, I've generally found the amount of control players have over that rate is fairly low. See also some great work here from James Grayson (h/t to 11tegen11 for the tip).

One of the landmark pieces of research in baseball asserted a similar fact about what happened after the ball left the bat: balls tended to land fair or be out at a fairly random rate for an individual player, but at an approximate constant for the league. Many didn't  - and don't - believe the data to this day but it's been shown that year-on-year players can rank very highly and then very low in terms of getting the ball to land in the field of play and I believe a fuller investigation into shots on target will show a similar result (before any baseball fans jump in here, I understand BABIP is more complicated than that, but for simplicity's sake, I think that's a fair summary).

Now, kicking a ball is obviously not the same as hitting a ball, but there are stark similarities between the two events. Firstly, many shots take place with very little thought time, especially those played into the box. The skill to get these on target is undoubtable, but the ability to 'place' them in the corner? Less convincing. Second, the positioning of the defense and particularly the goalkeeper is outside of an attacking player's control. This can be in the form of a great save in the top corner, but also from hard shots ricocheting off defenders knees or poor headers looping over a diving keeper. Given that we're often only talking about ~100-140 shots and 10-15 goals in a season, these few anomalous and 'lucky' events can have a huge bearing on the outcome.

Until I see reason to change it, I will therefore use a league average conversion rate of shots on target into goals, splitting chances between those inside and outside the box.

Now we've established what a player has done and what he should have done to date on an individual basis, let's turn our attention to what his data means to his team and how this translates to future success.

3. Who has he faced?
In the past I have accounted for this simply based on goals scored/conceded but given the reliance on shot data for individuals, it seems like that is the best path to take for teams too.

The question, yet again, becomes whether we should look at total shots, shots inside the box or shots on target. The answer really lies in a chicken and egg like discussion on what dictates the type of shots a team will take during a game more: an attacking team's desire to take shots inside the box or the defensive team's ability to force long range efforts? That needs a whole other case study, so for now I'm going to crudely assume it's somewhere in the middle. We can generate an expectation of total shots, shots inside the box (and hence outside) as well as shots on target by looking at what, on average, a player/team has done against each opponent compared to the league average. For example, let's assume Southampton are playing West Ham at home this week. The calculation would look something like:

Note: those opponent averages are as one GW7 and not backdated to when the game took place. Given the risk of small sample, I'm okay with this.

So, to date, Southampton are underperforming the league average by 8% in total shots (3% in, 13% out). This means that when forecasting games, we would reduce the average shots surrendered by their opponents by 3% for those inside the box and 13% for those outside. With the inside-the-box numbers being so low, we can essentially conclude that Southampton are holding opponents to their average level, at least at home.

We also need to think about how a team's success impacts an individual player. Previously I have somewhat crudely looked at the percentage of goals a player has 'accounted' for and then used a team's weekly forecast to estimate a player's own success. Instead of goals we can look at shots, but then it starts to get a touch tricky. Let's look at an example (through 7 weeks this season):

TOTAL SHOTS	Home	Away
Lambert	13	3
Southampton	61	31
Lambert %	21%	10%
INSIDE BOX
Lambert	8	3
Southampton	35	17
Lambert %	23%	18%
ON TARGET
Lambert	5	2
Southampton	20	10
Lambert %	25%	20%

Table 4 - Percentage of shots type taken by Rickie Lambert to date HTML Tables

What do with this data is a dilemma  Should we use all three averages? Just look at shots on target? Create some sort of average? Based on Lambert alone we clearly need to differentiate between home and away data but after that it's less clear. I'd be open to suggestions here, but for ease, if nothing else, my plan is to look at the percentage of a team's shots inside/outside a player has and then use his own individual on-target rate (or where unavailable the league average) to determine how many will hit the target. We then apply this to who the individual player faces this week, or beyond . . .

The actual forecast
We can summarise the above points with an example for how we might forecast a player's totals for the upcoming week. Let's stick with Lambert as we have his data to hand, and we'll assume he's facing West Ham at home.

First, we work out how we think Southampton will fare in the game. To date, away from home, West Ham are surrendering 11 shots inside the box per game and 5.7 outside. Our adjustments from above (table 3) suggest that these totals should be slightly revised downwards, giving us forecast totals of 10.7 shots inside the box and 4.9 outside.

Of these, Lambert is forecast to have 23% of those shots inside the box, so 2.45, and 19% of those outside the box, so 0.9 (table 4).

At this stage, we could get involved in Lambert's individual conversion rates, but given that he's spent a good portion of his career to date knocking around the Second Division, he's going to get the league average rate. That means (from table 1), we're giving him 2.45 shots inside the box*20% + 0.9 outside the box*7% for a total of 0.6 forecast goals, which by the way is an excellent number (after all that would equate to 23 goals over a 38 game season).

So that's how the new player forecast data will work for goals, with a similar approach for assists which I will write up shortly. I realise that this isn't rocket science and probably isn't doing much more than a lot of you already do on your own, but I thought it was important to setout the starting point for a new model, that will hopefully continue to develop over the season.

On that, I now pass it over to you for a while. How can the model be improved? What extra factors should we include? Should any of the above process be changed? Be gentle, and I look forward to reading your suggestions. Next I'll look at assists and then move onto to tweaking some of the ratios we're going to use, such as the league averages, player historic rates etc. Oh, and congrats for getting through all that if you made it this far.